Sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method

Abstract

The invention discloses a sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method, and the method comprises the steps: calculating a modulus depth function hypothesis space through employing a finite difference method based on a prior sound velocity profile and a horizontal wavenumber hypothesis interval; preprocessing the vertical array data to a frequency domain, constructing a linear underdetermined equation set about the frequency domain vertical array data and a modulus depth function of a hypothesis space under sparse constraint, and solving by using a sparse Bayesian learning algorithm to obtain estimation of a horizontal wave number spectrum; performing spectrum peak search on the horizontal wave number spectrum, estimating the order and the horizontal wave number of an actual excitation mode, and estimating a mode depth function of each order of mode by using a finite difference method; vertical array copy sound fields under different depths and horizontal distances are calculated according to a normal wave sound field formula; and respectively performing conjugate transpose multiplication on the vertical array copy sound field and actual data to obtain a depth-horizontal distance ambiguity surface, and searching the position of the maximum surface value as the estimation of the depth and horizontal distance of the source.

Description

Technical Field

[0001] The invention belongs to the technical field of target detection, and in particular relates to a sparse Bayesian learning method for passively estimating the depth and horizontal distance of shallow-water targets. Background Art

[0002] The passive estimation of the depth and horizontal distance of shallow-water targets has always been a difficult problem in underwater acoustic signal processing. Because the depth and horizontal distance information of shallow-water targets are mainly contained in the normal mode sound field in the vertical direction, model-driven methods represented by matching field processing require accurate ocean environment parameters (mainly including three types of sound velocity profile, sea depth and seabed characteristic parameters) to simulate the normal mode sound field as a copy, and then correlate the vertical receiving array data and the copy to estimate the target depth and horizontal distance. In actual situations, the measurement cost of seabed parameters is very high and often difficult to obtain. In addition, the sea depth obtained by checking the sea chart is not accurate enough. The uncertainty of these two types of parameters will lead to a mismatch between the modeled sound field and the actual data, further resulting in serious position estimation errors or even complete estimation failures. In this context, there are endless studies on passive positioning methods for shallow-water targets under unknown seabed characteristics and precise sea depth.

[0003] In order to solve the problem that the modeled sound field in traditional passive positioning methods is prone to mismatch with the actual data, the existing widely studied methods are machine learning / deep learning, and the models used include support vector machines, deep neural networks, etc. This type of method directly learns the mapping relationship between data and target positions, and does not require prior ocean environment parameters, but requires a large amount of reliable labeled data as a training set, which is relatively difficult to obtain in the field of underwater acoustics. In addition, the trained model has weak generalization ability and is not interpretable, which limits its application in ocean environments with obvious spatial and temporal variations. Summary of the invention

[0004] The purpose of the present invention is to provide a sparse Bayesian learning method for passively estimating the depth and horizontal distance of shallow-water targets in the case of unknown seabed characteristics and precise sea depth, so as to solve the problem that the traditional method for passively estimating the depth and horizontal distance of shallow-water targets (matching field processing) proposed in the background technology requires accurate ocean environment parameter modeling to copy the sound field, while the difficulty in obtaining seabed characteristic parameters and precise sea depth in practice often leads to mismatch in matching field processing.

[0005] To achieve the above object, the present invention provides the following technical solutions:

[0006] A sparse Bayesian learning method for passively estimating the depth and horizontal distance of shallow-water targets comprises the following steps:

[0007] Step 1, based on the prior sound velocity profile and horizontal wave number hypothesis interval, the mode depth function hypothesis space is calculated using the finite difference method based on wave equation solution;

[0008] Step 2: preprocess the vertical array data into the frequency domain, construct a linear underdetermined system of equations about the frequency domain vertical array data and the modulus depth function of the hypothesis space under sparse constraints, and solve them using a sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum;

[0009] Step 3, perform a peak search on the estimated horizontal wavenumber spectrum, estimate the order and horizontal wavenumber of the actual excited mode, and use the finite difference method to estimate the mode depth function of each order mode;

[0010] Step 4, calculating the vertical array copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula;

[0011] Step 5, conjugate transpose multiply the vertical array copy sound field without depth and horizontal distance with the actual data respectively to obtain the depth-horizontal distance ambiguity surface, and find the position of the surface maximum value as the estimation of the depth and horizontal distance of the source.

[0012] Preferably, in step 1, the method for obtaining the horizontal wave number hypothesis interval comprises the following steps:

[0013] According to the frequency point value and the sound speed, the horizontal wave number k corresponding to the depth function of each order mode excited by the ocean waveguide at this frequency point is determined. r The interval 2πf / c b ≤k r ≤2πf / c w , where c w is the minimum sound velocity in the water layer, c b is the seabed sound velocity, and the interval is sampled at equal intervals to obtain the horizontal wave number hypothesis interval [2πf / c b ]≤[k r1 , k r2 , ..., k rm , ..., k rM ]≤[2πf / c w ], M is the total number of sampling points of horizontal wavenumber in the assumed interval.

[0014] Preferably, in step 1, the calculation process of the module depth function hypothesis space is:

[0015] Linear interpolation of the sound velocity profile is used to obtain c(z i ), i=1, 2,...,I, where z i =ih, h is the depth interval between two difference points, I is the total number of sampling points after interpolation;

[0016] Based on the finite difference method for solving the wave equation and the assumption of absolute soft sea surface, the mode depth function corresponding to each sampling point in the horizontal wavenumber hypothesis interval is solved, and all mode depth functions are sampled according to the depth of each array element in the vertical array to obtain the mode depth function hypothesis space.

[0017] Preferably, step 2 comprises the following steps:

[0018] Step 2.1, read the vertical array data, divide each array element into time frames, and perform a windowed discrete Fourier transform to extract the frequency points of interest on the spectrum to obtain the multi-snap vertical array data y(f) in the frequency domain;

[0019] Step 2.2, construct the linear underdetermined equation system Where y(f) is the vertical array data preprocessed to the frequency domain, with a dimension of J×1, where J is the number of vertical array elements; w = [w1, w2, ..., w m , ..., w M ] is the horizontal wave number spectrum to be estimated; Φ m (z j , k rm ) is the horizontal wave number k rm The corresponding module depth function is at the jth array element depth z j The sampling value at ; n is the noise term;

[0020] In step 2.3, the sparse Bayesian learning algorithm is used to solve and obtain an estimate of the horizontal wavenumber spectrum.

[0021] Preferably, step 3 comprises the following steps:

[0022] Search the horizontal wavenumber spectrum Each spectral peak in the spectrum is considered to have a peak position [k r1 , …k rp , …, k rP ] is the estimate of the horizontal wave number corresponding to each order of actual excited modes, where P is the number of spectral peaks, that is, the number of actual excited modes;

[0023] Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k r1 , …k rp , …, k rP ], and sample all the modulus depth functions according to the depth of each element of the vertical array to obtain the estimation of the modulus depth function [Φ1, ...Φ p ,…,Φ P ].

[0024] Preferably, step 4 comprises the following steps:

[0025] Input depth z s , horizontal distance r s , vertical array element depth vector z, horizontal wave number estimate [k r1 , …krp , …, k rP ] and the modulus depth function estimates [Φ1, …Φ p ,…,Φ P ], and calculate the copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula: And p is normalized to p=p / ||p||2.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] The finite difference method is used to calculate the mode depth function corresponding to different horizontal wavenumbers. On this basis, sparsity constraints are introduced, and a horizontal wavenumber spectrum estimation method based on sparse Bayesian learning is proposed. The simple normal wave acoustic field structure of different depths and horizontal distances is reconstructed based on the horizontal wavenumber spectrum and mode depth function estimation, which is further used for passive estimation of target depth and horizontal distance. The present invention does not rely on seabed parameters and precise sea depth, requires a smaller amount of data and does not require depth and horizontal distance labels. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 It is a flow chart of the present invention.

[0029] Figure 2 This is the schematic diagram of data preprocessing.

[0030] Figure 3 Schematic diagram of the sparse Bayesian learning algorithm.

[0031] Figure 4 This is a schematic diagram of the data processing program interface based on MATLAB.

[0032] Figure 5 Schematic diagrams of the estimation results of the horizontal wavenumber spectrum and the excitation mode depth function, respectively.

[0033] Figure 6 Schematic diagram of the target depth and horizontal range ambiguity surface. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work belong to the protection scope of the present invention.

[0035] Reference Figure 1As shown, the present invention provides a sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method under the conditions of unknown seabed characteristics and precise sea depth. The method mainly includes a horizontal wavenumber spectrum estimator, and a source depth and horizontal distance estimator based on the horizontal wavenumber spectrum estimator.

[0036] Specifically, the sparse Bayesian learning shallow water target depth and horizontal distance passive estimation method includes 6 steps.

[0037] Step 1: Based on the prior sound velocity profile and horizontal wave number hypothesis interval, the finite difference method is used to calculate the mode depth function hypothesis space.

[0038] The specific process of this step is as follows:

[0039] Step 1.1: Determine the horizontal wave number k corresponding to the depth function of each order mode excited by the ocean waveguide at this frequency according to the frequency value and sound speed. r The interval 2πf / c b ≤k r ≤2πf / c w , where c w is the minimum sound velocity in the water layer, c b is the seabed sound velocity, and the interval is sampled at equal intervals to obtain the horizontal wave number hypothesis interval [2πf / c b ]≤[k r1 , k r2 , ..., k rm , ..., k rM ]≤[2πf / c w ], M is the total number of sampling points of horizontal wavenumber in the hypothesis interval, and m is the index of the sampling point;

[0040] Step 1.2: Linearly interpolate the sound speed profile (SSP) data to obtain c(z i ), i=1, 2,...,I, where z i =ih, h is the depth difference between two interpolation points, I is the total number of sampling points after interpolation;

[0041] Step 1.3, based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, solve the assumed interval of horizontal wave numbers [2πf / c b ]≤[k r1 , k r2 , ..., k rm , ..., k rM ]≤[2πf / c w ] Each sampling point (horizontal wave value) k rm , m=1, 2, ..., the module depth function corresponding to M is as follows:

[0042] Φ m(0, k rm )=0,

[0043] Φ m (z1,k rm ) = h,

[0044]

[0045] Φ m (z i , k rm ) is the horizontal wave number k rm The corresponding modulus depth function at depth z i The sampling value at i ) is the sound velocity profile after interpolation at depth z i The sampling value at , I is the total number of sampling points after interpolation; h is the interval between two depth interpolation points;

[0046] Step 1.4, sample all the modulus depth functions according to the depth of each element of the vertical array to obtain the modulus depth function hypothesis space.

[0047] Step 2: preprocess the vertical array data into the frequency domain, and construct a modulus depth function [Φ1, Φ2, ..., Φ m , ..., Φ M ] is a linear underdetermined system of equations under sparse constraints, and is solved using a sparse Bayesian learning algorithm to obtain the estimated results of the horizontal wavenumber spectrum as follows Figure 5 (a) shown.

[0048] Reference Figure 2 As shown, the vertical array data preprocessing includes the following steps:

[0049] In this embodiment, MATLAB is used to read vertical array data, and N array data are divided into frames with a frame length of 1s and an inter-frame overlap rate of 50%, so as to obtain L frames of data in total. A windowed FFT is performed on each frame data of each array element to obtain a spectrum. The window function selects a Kasier window with a parameter of 4.7, and the complex sound pressure value of the frequency point of interest is extracted to obtain L snapshots of vertical array data in the frequency domain. Each snapshot contains N array elements and is a column of N×1 vectors.

[0050] In step 2 of the present invention, the frequency domain vertical array data can be regarded as the weighted sum of each mode depth function in the hypothesis space, which is expressed as:

[0051]

[0052] Among them, y(f) is the vertical array data preprocessed to the frequency domain, with a dimension of J×1, and J is the number of vertical array elements;

[0053] w=[w1,w2,...,wm , ..., w M ] is the horizontal wave number spectrum to be estimated; Φ m (z j , k rm ) is the horizontal wave number k rm The corresponding module depth function is at the jth array element depth z j The sampling value at ; n is the noise term.

[0054] Since the number of mode depth functions in the hypothesis space is often much larger than the number of array elements, the system of equations is underdetermined. Since the number of modes actually excited is very limited and much smaller than the number of mode depth functions in the hypothesis space, the solution w of this linear underdetermined system of equations is sparse. At this time, the problem of estimating the horizontal wavenumber and mode depth function can be transformed into a linear underdetermined inverse problem under sparse constraints.

[0055] Reference Figure 3 As shown in the figure, the sparse Bayesian learning algorithm implementation includes the following parts:

[0056] ① Parameter prior distribution modeling, each element w in the parameter vector w to be determined m Modeled as having a mean of 0 and a variance of γ m The complex Gaussian distribution has independent elements and a variance of γ. m is an unknown number, and the vector w obeys a multivariate complex Gaussian distribution:

[0057]

[0058]

[0059] Γ=E[ww H ] = diag(γ)

[0060] ②Data likelihood distribution modeling, assuming that the frequency domain vertical array data y and the noise term n are independent of each other, and each element in n is independent of each other, and all obey the mean of 0 and the variance σ 2 Gaussian white noise with variance σ 2 is an unknown number, and the data likelihood distribution can be written as a multivariate complex Gaussian distribution p(y|w)=CN(y;Ψw,σ 2 I); Expanded to multiple snapshots

[0061]

[0062] ③ Random maximum likelihood method parameter estimation, multiply the parameter prior distribution and the data likelihood distribution and integrate to find the marginal distribution of parameter w It is called the second-likelihood distribution; the unknown parameters are obtained by maximizing the second-likelihood distribution Here, a fixed-point update algorithm with low computational complexity is used for parameter estimation. The code is as follows: Figure 5 shown.

[0063] ④ Calculate the posterior probability distribution of parameter w, which obeys Gaussian distribution:

[0064] The estimate of the parameter w is equal to the posterior mean μ w .

[0065] In the present invention, how to use the sparse Bayesian learning algorithm to solve the linear underdetermined inverse problem is a conventional technical means in the field, and those skilled in the art will not elaborate on it.

[0066] Step 3: Perform a peak search on the estimated horizontal wavenumber spectrum to estimate the order and horizontal wavenumber of the actual excited mode, and use the finite difference method to estimate the mode depth function of each order mode.

[0067] In step 3 of the present invention, the horizontal wave number spectrum is obtained by solving the linear underdetermined inverse problem based on the sparse Bayesian learning algorithm in step 2. Then, search the horizontal wavenumber spectrum Each peak in the spectrum is obtained by r1 , …k rp , …, k rP ], that is, the estimated result of the horizontal wave number corresponding to each order of actual excitation mode, where P is the number of spectral peaks, p represents the index, that is, the number of actual excitation modes, according to the horizontal wave number estimation result [k r1 , …k rp , …, k rP ] and the finite difference method to calculate the corresponding module depth function [Φ1,…Φ p ,…,Φ P ], the specific process is:

[0068] Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k r1 , …k rp , …, k rP ] each sampling point k rp The corresponding modulus depth function is obtained by sampling all modulus depth functions according to the depth of each element of the vertical array to obtain the estimation of the modulus depth function [Φ1, ...Φ p ,…,Φ P ]like Figure 5 (b) as shown.

[0069] Step 4: Calculate the vertical array copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula.

[0070] In step 4 of the present invention, the input depth z s , horizontal distance r s, vertical array element depth vector z, horizontal wave number [k r1 , …k rp , …, k rP ] and the module depth function [Φ1,…Φ p ,…,Φ P ], and calculate the copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula: The attenuation effect of each mode is neglected, and P is normalized to P=P / ||P||2.

[0071] Step 5: Correlate the vertical array copy sound field without depth and horizontal distance with the actual data (conjugate transpose multiplication) to obtain the depth-horizontal distance ambiguity surface. The calculation process is as follows:

[0072]

[0073] Among them, B(z s , r s , f) is the ambiguity surface at frequency f, p(z s , r s ) is the depth z after normalization s , horizontal distance r s The corresponding copy sound field, y(f) is the vertical array data in the frequency domain; the position of the maximum value of the ambiguity surface is found as the estimate of the depth and horizontal distance of the source.

[0074] Reference Figure 6 As shown, the location of the surface maximum value (that is, the reddest area in the figure) is the estimate of the depth and horizontal distance of the source.

[0075] The method of the present invention combines data-driven with model-driven, and uses the finite difference method and sound velocity profile to construct the model depth function hypothesis space; based on this, the formula of the normal mode solution of the wave equation is used to transform the horizontal wavenumber spectrum estimation into a sparse constrained linear underdetermined inverse problem; then the sparse Bayesian learning algorithm is used to estimate the horizontal wavenumber spectrum; and then the copy sound field is further constructed and the depth and horizontal distance of the target are estimated through a correlator. Compared with the traditional model-driven matching field processing method, it does not rely on seabed parameters and precise sea depth, and is more tolerant; compared with the data-driven machine learning / deep learning method, it requires a smaller amount of data and does not require depth and horizontal distance labels. In summary, the method proposed by the present invention can overcome the problem that marine environmental knowledge is difficult to effectively use in passive target positioning.

[0076] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A sparse Bayesian learning method for passive estimation of shallow sea target depth and horizontal distance, characterized in that: The following steps are involved: Step 1, based on the prior sound velocity profile and horizontal wave number hypothesis interval, the mode depth function hypothesis space is calculated using the finite difference method based on wave equation solution; Step 2: preprocess the vertical array data into the frequency domain, construct a linear underdetermined system of equations about the frequency domain vertical array data and the modulus depth function of the hypothesis space under sparse constraints, and solve them using a sparse Bayesian learning algorithm to obtain an estimate of the horizontal wavenumber spectrum; Step 3, perform a peak search on the estimated horizontal wavenumber spectrum, estimate the order and horizontal wavenumber of the actual excited mode, and use the finite difference method to estimate the mode depth function of each order mode; Step 4, calculating the vertical array copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula; Step 5, conjugate transpose multiply the vertical array copy sound field without depth and horizontal distance with the actual data respectively to obtain the depth-horizontal distance ambiguity surface, and find the position of the surface maximum value as the estimation of the depth and horizontal distance of the source.

2. A sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method as claimed in claim 1, characterized in that: In step 1, the method for obtaining the horizontal wave number hypothesis interval includes the following steps: According to the frequency point value and the sound speed, the horizontal wave number k corresponding to the depth function of each order mode excited by the ocean waveguide at this frequency point is determined. r The interval 2πf / c b ≤k r ≤2πf / c w , where c w is the minimum sound velocity in the water layer, c b is the seabed sound velocity, and the interval is sampled at equal intervals to obtain the assumed interval of horizontal wave number [2πf / c b ]≤[k r1 , k r2 , ..., k rm , ..., k rM ]≤[2πf / c w ], M is the total number of sampling points of horizontal wavenumber in the assumed interval.

3. A sparse Bayesian learning method for passive estimation of shallow sea target depth and horizontal distance as claimed in claim 1, characterized in that: In step 1, the calculation process of the module depth function assumption space is: Linear interpolation of the sound velocity profile is used to obtain c(z i ), i=1, 2,...,I, where z i =ih, h is the depth interval between two difference points, I is the total number of sampling points after interpolation; Based on the finite difference method for solving the wave equation and the assumption of absolute soft sea surface, the mode depth function corresponding to each sampling point in the horizontal wavenumber hypothesis interval is solved, and all mode depth functions are sampled according to the depth of each array element in the vertical array to obtain the mode depth function hypothesis space.

4. A sparse Bayesian learning method for passive estimation of shallow sea target depth and horizontal distance as claimed in claim 1, characterized in that: The step 2 comprises the following steps: Step 2.1, read the vertical array data, divide each array element into time frames, and perform a windowed discrete Fourier transform to extract the frequency points of interest on the spectrum to obtain the multi-snap vertical array data y(f) in the frequency domain; Step 2.2, construct the linear underdetermined equation system Where y(f) is the vertical array data preprocessed to the frequency domain, with a dimension of J×1, where J is the number of vertical array elements; w = [w1, w2, ..., w m , ..., w M ] is the horizontal wave number spectrum to be estimated; Φ m (z j , k rm ) is the horizontal wave number k rm The corresponding module depth function is at the jth array element depth z j The sampling value at ; n is the noise term; In step 2.3, the sparse Bayesian learning algorithm is used to solve and obtain an estimate of the horizontal wavenumber spectrum.

5. A sparse Bayesian learning shallow sea target depth and horizontal distance passive estimation method as claimed in claim 1, characterized in that: The step 3 comprises the following steps: Search the horizontal wavenumber spectrum Each spectral peak in the spectrum is considered to have a peak position [k r1 , …k rp , …, k rP ] is the estimate of the horizontal wave number corresponding to each order of actual excited modes, where P is the number of spectral peaks, that is, the number of actual excited modes; Based on the finite difference method for solving the wave equation and the assumption of an absolutely soft sea surface, the horizontal wave number estimate [k r1 , …k rp , …, k rp ], and sample all the modulus depth functions according to the depth of each element of the vertical array to obtain the estimation of the modulus depth function [Φ1, ...Φ p ,…,Φ P ].

6. A sparse Bayesian learning method for passive estimation of shallow sea target depth and horizontal distance as claimed in claim 1, characterized in that: The step 4 comprises the following steps: Input depth z s , horizontal distance r s , vertical array element depth vector z, horizontal wave number estimate [k r1 , …k rp , …, k rP ] and the modulus depth function estimates [Φ1, …Φ p ,…,Φ P ], and calculate the copy sound field at different depths and horizontal distances according to the simple normal wave sound field formula: And normalize p to p=p / ||p||2.

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